Glance at the summary firstThe summary from the end of the lesson, as a road map before you start reading.
As light moves away from its source, it spreads over an area that grows larger and larger; that is why when the distance from a small, point source doubles, the light drops to a quarter, that is, by two stops, and when it grows about one and a half times, it drops by one stop. The sun is so far away that a change of distance of a few steps changes nothing, while close to a large window light decreases more slowly than the law says; the real deciding factor is the ratio of the distances of the things in the frame from the source. Bringing the subject close to the source and keeping the background far gives a strong subject–background separation, moving the source away or putting everyone at an equal distance gives even light; and this equality is the way to protect the detail of faces of every skin tone in a group.
Learning goal
You will be able to explain why light weakens so fast as it moves away from its source through the spread of light over a surface, and use this knowledge to predict in advance how much light the subject, the background and the people in a group will receive. You will see that the inverse square law holds for small, point sources, calculate that two stops of light are lost when the distance doubles and one stop when it grows about one and a half times, know why the sun behaves as if it weren't affected by this law and why the falloff is slower when you are close to a large window, understand that the real deciding factor is the ratio of the distances, and with this ratio manage the subject–background separation, the even lighting of a group and the detail of faces of every skin tone, moving the source closer or farther depending on whether you want a dark background or even light.
The question
In the evening, in a corner of the park, you are shooting a portrait of two friends under a single streetlamp. One stands right beside the lamp, the other a few steps behind. On the screen the face of the one in front is almost pure white, while the face of the one behind is lost in the darkness; there are only a few steps between them. When you tell the one behind to come one step forward, their face suddenly lights up; when you tell the one in front to step back one step, their face fades.
How does a difference of a few steps create such a big difference in light? Why does light weaken so fast as it moves away? In this lesson we will talk about the inverse square law, the situations where it holds and where it doesn't, and using distance as a lighting tool.
Context
In Lesson 8.8, while getting to know the stop, we saw the basic rule of the inverse square law: when the distance from a small source doubles, the light drops to a quarter. There, this was a calculation for bringing a lamp closer to open up a face. This lesson turns the same law into a tool for shaping light: it tells why it is so, where it doesn't work, and how, by choosing distances deliberately, to decide what stays lit and what stays dark in the frame.
In natural light you most often can't move the sun; but you can place your subject and yourself relative to a window, a doorway, a streetlamp or a lantern. Knowing how distance changes light also decides where to put the reflectors and diffusers you will see in the coming lessons.
Simple explanation
Why does light decrease with the square?
Light spread is the light coming out of a source being distributed over an area that grows larger and larger as it moves away. Think of a can of spray paint: when you hold it close to the wall, it makes a small, dark spot; when you spray from twice as far, the same paint spreads over an area twice as wide and twice as high, that is, four times as large, and the spot is much lighter. Light is like this too: when the distance doubles, the same light spreads over an area four times as large, and a quarter of it falls on each point.
A point source is a source that looks small compared to its distance from the subject, like a bulb, a lantern or a distant streetlamp; the inverse square law works best with these sources. Thinking in stops makes the calculation easier: when the distance doubles, the light decreases by two stops, when it quadruples, by four stops. When the distance grows about 1.4 times, on the other hand, the light halves, that is, decreases by one stop. Pulling back from one meter to two meters gives the same loss of light as pulling back from two meters to four meters; what matters is not the difference in meters, but their ratio.
Why do the sun and large sources behave differently?
The sun is so far from Earth that going a few meters forward or back in a park changes the distance to it only by an unmeasurably small ratio. That is why in sunlight moving the subject closer to or farther from the source doesn't change the exposure; everything standing in an open area receives light of the same intensity. In the sun, what creates differences in brightness isn't distance, but shade and angle.
The near field is the region closer to a large source, like a window or an opening of cloudy sky, than a few times its size. In this region, light decreases with distance more slowly than the inverse square law says; to the subject, the source isn't a small point but a wide surface. Getting closer to a window still increases the light, but not as sharply as getting closer to a bulb. That is why a face lighting up as it takes a step toward the edge of the eaves is real, but the calculation doesn't follow the square rule exactly; you need to look at the screen or the meter.
What does the distance ratio decide?
The distance ratio is the ratio of the distances of two things in the frame from the source, and it decides the difference in light between them. If there is a wall three meters behind a subject one meter from a lamp, the wall is four meters from the source; the ratio is four, the difference in light is four stops, and the wall sinks into darkness. If the same subject and wall stood four and seven meters from the lamp, the ratio would be about one point seven, and the difference about one and a half stops. As the source moves farther away, the brightness of the things in the frame comes closer together.
Subject–background separation is the difference between the brightness of the subject and the brightness of the background, and it is built with the distance ratio. If a dark, plain background is wanted, it is enough to bring the subject close to the source and keep the background far; that is why the room behind someone sitting right by a window looks dark. If even, flat light is wanted, the source is moved away, or the subject is brought closer to the background. Which one is right depends on what the photo wants to say; but if the distances are known, the result can be predicted in advance.
How are groups and skin tones protected?
When the people in a group stand at different distances from the source, the same law lights them differently: there are two stops of difference between a person one meter from the source and a person two meters away. This difference becomes even more visible in a frame where people of different skin tones stand side by side: while the forehead of a light-skinned person standing close to the source blows out, the face of a dark-skinned person standing far away can lose its detail inside the shadow. The solution to this is to place people not according to their skin, but at an equal distance from the source.
Gathering the group on an arc around the source, with everyone at about the same distance, or if possible moving the source away from the group, brings the distance ratios close to one. When the source is four and five meters away, the difference between two people is a little over half a stop; when it is one and two meters away, it is two stops. Then setting the exposure so that the brightest face doesn't blow out and the darkest face still carries detail shows every face as it is, neither blown out nor darkened.
Visual evidence
The next evening you go under the same streetlamp with a measuring tape. First, from far enough away that you can easily count the lamp's light as a point source, you meter your two friends standing at distances of one and a half meters and three meters: the ratio is two, the difference two stops. Your freckled, light-skinned friend was in front; their forehead was giving a clipping warning on the screen. Your dark-skinned friend was behind; the shadow side of their face had melted into the dark.
You place the two of them on an arc around the lamp, so that both stand about three meters away. In the metering, almost no difference remains between the two faces; you set the exposure so that your light-skinned friend's forehead doesn't blow out and detail remains on your dark-skinned friend's cheek. Then, for a solo portrait, you bring your dark-skinned friend to one and a half meters from the lamp, and the bushes behind them stay four and a half meters from the lamp: the ratio is three, the difference a little more than three stops. The bushes sink into darkness; their face, with the warm brown of their skin and the glint of the lamp in their eyes, shines on its own in front of a dark background.
Common mistakes
Common mistakeLining up a group at different distances from a small source.
The person close by blows out, the one far away darkens. The fix: place everyone at about the same distance from the source, on an arc, or move the source away.
Common mistakeTrying to change the brightness in sunlight by moving the subject a few steps closer or farther.
The sun is so far away that these steps make no difference. The fix: in the sun, manage brightness not with distance, but with shade, angle and a reflector.
Common mistakeTrusting the inverse square calculation blindly right by a large window.
In the near field, light decreases more slowly. The fix: when close to large sources, look at the meter and the screen, and use the calculation for small sources.
Summary
As light moves away from its source, it spreads over an area that grows larger and larger; that is why when the distance from a small, point source doubles, the light drops to a quarter, that is, by two stops, and when it grows about one and a half times, it drops by one stop. The sun is so far away that a change of distance of a few steps changes nothing, while close to a large window light decreases more slowly than the law says; the real deciding factor is the ratio of the distances of the things in the frame from the source. Bringing the subject close to the source and keeping the background far gives a strong subject–background separation, moving the source away or putting everyone at an equal distance gives even light; and this equality is the way to protect the detail of faces of every skin tone in a group.
Mini assignment
In this assignment you will use distance as a lighting tool.
- Use a small lamp or a lantern in a dark room; put an object one, one and a half, two and four meters from the lamp and note in stops how much the metering changes at each.
- Make the same measurement in front of a large window, very close to the window and a few meters away; compare how the falloff differs from the lamp.
- Get a dark background by putting a subject close to the source and the background far; then get more even light by moving the source away.
- Shoot two people first at different distances from the source, then at an equal distance; compare the detail of the two faces.
Check yourself
- When the distance doubled, did the metering really change by two stops?
- Did the measurements in front of the window change more slowly than those in front of the lamp?
- Do the faces of the two people at an equal distance, even if their skin tones differ, both stand without blowing out or darkening?
Glossary
| Term | Short definition |
|---|---|
| Point source | A light source that looks small compared to its distance from the subject, where the inverse square law works best. |
| Light spread | The light coming out of a source being distributed over an area that grows larger as it moves away. |
| Distance ratio | The ratio of the distances of two things in the frame from the source; it decides the difference in light between them. |
| Near field | The region closer to a large source than a few times its size; here light decreases not with the square but more slowly. |
| Subject–background separation | The difference between the brightness of the subject and the brightness of the background. |
Mini quiz
1. When the distance from a small source doubles, what happens to the light falling on the subject?
- A) It drops to half
- B) It drops to a quarter
- C) It doesn't change
- D) It doubles
2. Why doesn't moving the subject a few steps closer in sunlight change the exposure?
- A) The sun is so far away that a few steps change the distance ratio too little to notice
- B) Because sunlight is colored
- C) Because the camera can't meter the sun
- D) Because the sun is a near-field source
3. If the subject is one meter from a lamp and the wall behind it four meters away, about how many stops darker is the wall than the subject?
- A) One stop
- B) Two stops
- C) Zero stops
- D) Four stops
4. Under a streetlamp, a light-skinned friend stands close and a dark-skinned friend far away; one blows out, the other darkens. What should you do?
- A) Set the exposure only for the one close by
- B) Take the one far away out of the frame
- C) Place the two of them at an equal distance from the lamp, on an arc, and set the exposure for both faces
- D) Fire the flash at full power
Answers
- B — The light spreads over an area four times as large; that is two stops.
- A — Next to the distance to the sun, a few meters are nothing.
- D — The ratio is four, the square of four is sixteen; one sixteenth comes to four stops.
- C — An equal distance keeps the two faces in the same light; the exposure can be set for both at once.
Summary card
- Light spreads: distance ×2 → area ×4 → light ¼, two stops.
- Distance ×1.4 → one stop; what matters is not the meters but the ratio.
- In the sun a few steps make no difference; close to a large window the falloff is slower.
- Bring the subject close to the source, keep the background far: a dark background. Move the source away: even light.
- Line up the group at an equal distance from the source; let every face appear with its own skin.
Bridge to the next lesson
In the solo portrait you shot under the streetlamp, the side of your friend's face turned toward the lamp is warm and detailed, but their other cheek has sunk into darkness. You can't move the lamp, and you don't want to turn their face to the light either; that half shadow has character, but it is a little too dark. Could there be a simple way to send light back to the shadow side of the face? What is a white card good for? The next lesson talks about reflectors, and how white, silver and gold surfaces carry light back into the shadow.